Our experience with the 4900 is that it takes up to 50 head cleanings to move flush from the cart to the print head. doing so will move the same amount of ink in all the other positions as the INITIAL CHARGE. What will be missing of course is the prolonged suction of an INITIAL CHARGE which takes about 7-8 minutes to complete. The 50 head cleanings will take you probably some hours. These are little sips of ink at a time.
Again - we can only recommend what we know works. We can advise you in what you would rather try on your own if we can. So, in that case, do NOT use powerful paired cleanings as there is a legitimate advisory that the use of many in a row is damaging to the print head.
The service program is a great tool and it is too bad that the Epson repair people only use Windows machines. But it is still what is most effective.